The fluctuations of loads and renewable power plants can make the power system operate without meeting the n−1 criterion. In this paper, we propose a node indispensability estimation (NIE) model based on the Graph Attention Network (GAT) for risk early warning. The existence of the indispensable component for specific operation conditions is predicted whose independent removal causes overloading. Considering the difficulty to place monitoring units on all system components, the state information of a part of the buses is used as input for the NIE model. The GAT is compared with other neural network algorithms such as Graph Convolutional Networks (GCN) and Multilayer Perceptron (MLP). Simulation results in IEEE test systems show that the proposed model based on GAT has sufficiently high prediction accuracies in estimating the node indispensability with partial state observations. Our work provides useful warnings for power operators to improve the system operation condition to secure sufficient safety levels.